Measurement of the molecular weight distribution of polymers is an important part of polymer characterization and is of great interest to those studying, developing, or producing synthetic or natural polymers. One of the most accurate methods for measuring the molecular weight distribution of a sample is to use size exclusion chromatography to separate the polymers by size in a flowing system and then to use a light scattering detector to measure the molecular weight of each eluting fraction. The separation by size becomes a separation in time as the largest molecules flow out of the end of the chromatographic system first, followed by slightly smaller molecules, with the smallest molecules coming last. The profile of the polymer concentration versus time at a point along the flow generally consists of one or more smooth peaks. If the original sample consists of a wide continuous range of molecular weights, there will be a single very broad peak and the sample is said to be polydisperse. If the sample was very homogeneous and only had a very small range of molecular weights, the peak is narrow and the sample is described as being monodisperse. An important concept is that of a slice, defined as an instantaneous short section of flow along which the polymer is homogeneous and the concentration constant. A peak is composed of many slices arranged end to end.
As the molecules in their solvent flow out of the chromatographic system they may flow next into light scattering detection instrumentation which produces electrical signals proportional to the light scattered in various directions by the scattering sample. In this way, the molecular weight can be determined as a function of time and then related back to the distribution of molecular weight in the polymer sample. In order to determine the molecular weight, however, an additional measurement is necessary, namely the sample concentration as a function of time.
The most common way to measure the concentration as a function of time is to use a refractive index detector to measure the change in refractive index which is proportional to the polymer concentration. In practice, this is always done in a second instrument downstream from the light scattering instrument. The information that is necessary to determine molecular weight is the light scattering,intensity extrapolated to zero scattering angle and the concentration for each slice. In particular, it is necessary to match each slice of the extrapolated light scattering intensity with the corresponding slice of the concentration signal.
The light scattering and concentration signals are produced by two different instruments separated by a short length of tubing. This means there will be a time delay between corresponding slices which must be determined. In addition, the connecting tubing as well as the flow cells of the two instruments create some mixing of the flow which tends to degrade the polymer separation/fractionation performed by the chromatographic system. In other words, it broadens the peak. This effect is called interdetector band broadening, in contrast to traditional column band broadening, and underscores the fact that the concept of a slice is not completely valid. A short section of flow does not remain unchanged as it travels through the system, but mixes somewhat with other slices during its passage from one detector to the next. It is not possible, therefore, to measure both the light scattering and concentration of the same slice since the same slice cannot exist at both locations. The contamination of a slice with sample fractions from other slices as it travels from one detector to another will create errors in the measurement of the molecular weight distribution. The effect of interdetector band broadening must be kept small to minimize measurement errors for samples of small polydispersity. When samples span a broad, continuous range of molecular weights, such interdetector band broadening effects are rarely noticed and usually are of little importance.
Interdetector band broadening has deleterious effects in all chromatography systems containing more than a single detector and efforts to reduce it have a substantial history. The broadening due to flow in long tubes has been well studied and it is known that the effect is greatly reduced by using very small diameter tubes. For this reason, standard fluid chromatography tubing is now made with an inside diameter of 0.25 mm which is the smallest practical size. The broadening due to optical flow cells is highly dependent on the flow pattern inside the cell and hence highly dependent on the design. In general, the smaller the cell volume, the smaller the broadening. In cells designed for refractive index detectors, as well as in other optical instruments such as light scattering detectors, there are at least two factors which limit how small the cell volume can be. One is the optical path length of the light beam through the cell. Usually the sensitivity of the detector will be proportional to the optical path length so it cannot be made very small. The other factor limiting the miniaturization of the flow cell is the optical beam diameter. The optical beam, especially if not generated by a laser, often cannot be made smaller than a certain dimension. These two minimum dimensions define a minimum cross section. If the sample flow is perpendicular to the optical beam, as is often the case, then the volume will be determined by the product of the minimum cross section and the length along the flow. This length will in general be limited from below by some other practical consideration.
Even for a fixed volume, the broadening depends on the details of the structural geometry and how it affects the flow pattern. The region of introduction of the flow into a detection cell requires particular attention. Since the flow will generally be introduced from a very small diameter tube, the cross section of the flow will be initially very much smaller than the minimum cross section of the cell as determined by the optical path length and beam diameter. This will generally cause the flow to become non-laminar and create eddies. These eddies can extend the full length of the flow cell. The flow reaches the far end of the cell, turns around, and flows back to the point of entry where it repeats the process. This rotational motion, or eddy, mixes flow between slices separated by multiples of the full volume of the flow cell and can cause serious interdetector band broadening.
In most discussions of interdetector band broadening, the phenomena are considered to be a random statistical process of solute mixing as discussed, for example, by W. W. Yau in his book Modern Size Exclusion Liquid Chromatography published by John Wiley & Sons in 1979. A detailed discussion by J. C. Dolan in his article published in volume 10 of LCGC, pages 20 through 25, in 1992 discusses many types of interdetector band broadening, but only in this same statistical sense. Thus the actual details of the flow eddies that occur whenever the diameters of the successive components change are neither discussed nor noted. All such band broadenings are treated as successive Gaussian broadenings of different weightings to yield an estimate of the contributions of each to the final total broadening. A particularly innovative element of our invention relates to our detailed experimental studies of the various eddy patterns that occur during the transition of flow from a very small diameter stream to one of much larger diameter such as occur within the optical detection cells. By studying these eddies, their formation and destruction, we have been able to address these interdetector band broadening effects and have developed methods and apparatus for their reduction, as shall be presented herein. In contrast to our approach, the traditional methods as described, for example, by Dolan are comprised of procedures to minimize such effects by using ". . . small injection volumes . . ., short runs of small internal diameter tubing that connect the column to the rest of the system, and a method-appropriate detector cell volume . . ." Our invention is directed to modify the detector cell volume. Martin, et al. discuss band broadening in the detector in their 1975 article in the Journal of Chromatography in volume 108 beginning on page 229.
There have been many inventions developed over the years concerned with the homogenization of two or more fluids that are to be mixed. Our invention is quite distinct from these earlier procedures as there is only a single fluid present in the detection cell but, because of its changing composition, the composition within the cell is correspondingly changing and often inhomogeneous. Although the flow in a detection cell is continuous with the flow in the inlet capillary bringing the sample to the cell, the spatial and temporal concentration distribution within the cell does not generally mimic the concentration distribution in the transferring capillary. The sharp temporal concentration changes within the capillary that transfers the separated sample into the detection cell results in a chaotic inhomogeneity of concentration within the detection cell itself, as has been discussed above. A very small diameter flow suddenly increases its cross section by many fold as it moves from the tube into the detection cell and undergoes a chaotic disruption within the whole cell volume. The basic objective and achievement of this invention is to confine this flow disruption to the smallest possible volume in the shortest possible time and not allow the entire cell to act as a large mixing chamber by eliminating spatially large scale eddies within the detection cell.